Solar thermal concentrator apparatus, system, and method

ABSTRACT

An apparatus is disclosed including: a trough shaped reflector extending along a longitudinal axis and including at least one reflective surface having a shape which substantially corresponds to an edge ray involute of the absorber.

CROSS REFERENCE TO RELATED APPLICATIONS

-   1. This application is a continuation application of non-provisional    patent application Ser. No. 13/153,802, titled “SOLAR THERMAL    CONCENTRATOR APPARATUS, SYSTEM, AND METHOD”, filed Jun. 6, 2011 in    the United States Patent and Trademark Office, which claims the    benefit of U.S. provisional patent application No. 61/385,890, filed    on Sep. 23, 2010 in the United States Patent and Trademark Office.-   2. The specifications of the above referenced applications are    incorporated herein by reference in their entirety.

STATEMENT OF RIGHTS UNDER THE INVENTION

This invention was made with government support. The invention was madewith the State of California's support under the California EnergyCommission contract No. 5005-05-21. The Energy Commission has certainrights to this invention.

BACKGROUND OF THE INVENTION

This disclosure relates to devices for the transmission of radiation,especially of light. In particular, it is related to a non-focusingreflector for the concentration of radiation such as sunlight at adesired region over a wide range of angles of incidence.

A number of systems for passive or non-tracking reflecting concentrationof solar energy have been produced in the past. Among such systems arethose shown in U.S. Pat. Nos. 5,537,991; 4,002,499; 4,003,638;4,230,095; 4,387,961; 4,359,265; 5,289,356; and 6,467,916, which are allincorporated by reference in their entirety. It is appropriate to referto the reflectors as light-transmission devices because it is immaterialwhether the reflectors are concentrating radiation from a large solidangle of incidence (e.g. concentrating solar light onto a solar cell) orbroadcasting radiation from a relatively small source to a relativelylarge solid angle (e.g. collecting light from an LED chip to form abeam).

Concentration of radiation is possible only if the projected solid angleof the radiation is increased. This requirement is the directconsequence of the law of conservation of the etendue, which is thephase space of radiation. Solar concentrators which achieve highconcentration must track the sun; that is, they must continuouslyreorient in order to compensate for the apparent movement of the sun inan earth center (Ptolemaic) coordinate system. Reflectors, in contrast,are fixed in position for most lighting purposes. For trackingcollectors the direction to the center of the sun is stationary withrespect to their aperture. Such concentrators can achieve very highconcentrations of about 45,000 in air. Even higher concentrations havebeen achieved inside transparent media.

Tracking, however, is technically demanding because solar collectors arecommonly fairly large and designing these systems for orientationalmobility may add significantly to their cost. Moreover, the absorber,which typically incorporates some heat transfer fluid as well as piping,also may need to be mobile. This is the motivation to study theconcentration which can be achieved with stationary, non-trackingdevices. The same principles apply when it is desired to deliver lightor other radiant energy from a small source to a relatively large solidangle.

SUMMARY OF THE INVENTION

The inventor has realized that a concentrator assembly may be used,e.g., to collect solar energy to produce heat. Embodiments of theconcentrator assembly feature a wide acceptance angle, allowing for usein non-tracking applications. Embodiments of the concentrator assemblyfeature a high collection efficiency (e.g., about 50% or greater) athigh operating temperatures (e.g., 150 C or more, 200 C or more, etc.).

In one aspect, an apparatus is disclosed for concentrating light to anelongated absorber including: a trough shaped reflector extending alonga longitudinal axis having at least one reflective surface having ashape which substantially corresponds to an edge ray involute of theabsorber.

In some embodiments, the reflector has a first side and a second sidedisposed symmetrically on opposing sides of an optic plane transversethe longitudinal axis. Each side of the reflector includes a reflectivesurface having a shape which substantially corresponds to an edge rayinvolute of the absorber.

In some embodiments, the absorber includes a cylindrical absorberextending in the direction of the longitudinal axis and disposed at thebottom of the trough shaped reflector.

In some embodiments, the reflector includes an entrance aperture locatedat a top of the trough. In some embodiments, substantially all lightincident on the entrance aperture at angles less than an acceptanceangle are concentrated to the absorber.

In some embodiments, the reflector concentrates light at thethermodynamic limit.

In some embodiments, the absorber is spaced apart from the reflector bya gap distance; and a portion of the reflector at the bottom of thetrough includes a reflective cavity having a reflective surface with ashape that deviates substantially from the edge ray involute of theabsorber.

In some embodiments, the cavity includes a V-shaped trough extendingalong the bottom of the reflector in the direction of the longitudinalaxis.

In some embodiments, the V-shaped trough includes an aperture positionedsuch that the image of the absorber reflected in a wall of the V-shapedtrough has a top which is positioned proximal or above the aperture ofthe V-shaped top in the direction extending from the top of the troughto the bottom of the trough.

Some embodiments are characterized by an efficiency loss averaged overthe acceptance angle relative to an equivalent gapless concentrator of0.02 or less.

Some embodiments are characterized by a concentration ratio equal to atleast 90% of that of an equivalent gapless concentrator.

In some embodiments, the gap distance is less than a radius of theabsorber.

In some embodiments, the reflector concentrates light to the absorberwith a concentration ratio C of 1.0 or greater, of 1.25 or greater, of1.5 or greater, of 1.75 or greater, of 2.0 or greater, or more.

In some embodiments, a reflective surface of the reflector has areflectivity of 90% or more for solar light.

In some embodiments, a reflective surface of the reflector has areflectivity of 94% or more for solar light.

In some embodiments, the reflector has an acceptance angle of at least25 degrees, at least 35 degrees, or at least 45 degrees, or at least 60degrees, or more.

In another aspect, an apparatus for concentrating light to an absorberis disclosed including: at least one reflective surface configured toreceive light incident at angles less than an acceptance angle andconcentrate the received light to the absorber. The concentrator ischaracterized in that substantially any light ray emitted from theabsorber would exit the concentrator without returning to the absorber.In some embodiments, at least one reflective surface includes a surfacewhich corresponds to an edge ray involute of the absorber.

In another aspect, an apparatus is disclosed for converting incidentsolar light to heat, including: an evacuated tubular enclosure extendingalong a longitudinal axis from a proximal end to a distal end; a tubularabsorber element located within the evacuated enclosure, and including aselective surface configured to absorb solar light incident through theevacuated enclosure and convert the solar light to heat; and a U-shapedtube in thermal contact with the absorber element. The U-shaped tube mayinclude: a fluid input and a fluid output located at the proximal end ofthe tubular enclosure; an input portion extending from the fluid inputalong an interior surface of the tubular absorber element; and an outputportion extending from the fluid output along an interior surface of thetubular absorber element; and a curved portion located proximal thedistal end of the enclosure and providing fluid communication betweenthe input and output portions. In some embodiments, the input portionand the output portion are spaced apart.

In some embodiments, fluid input into the fluid input at a firsttemperature travels though the U-shaped tube, absorbs heat from theselective absorber, and is output from the output at a secondtemperature higher than the first.

In some embodiments, the selective surface has an absorptivity of atleast 0.75 and an emissivity of 0.25 or less at temperatures greaterthan 100 C.

In some embodiments, the selective surface has an absorptivity of atleast 0.9 and an emissivity of 0.1 or less at temperatures greater than100 C.

In some embodiments, the selective surface has an absorptivity of atleast 0.9 and an emissivity of 0.1 or less at temperatures greater thanabout 200 C.

In another aspect, an apparatus is disclosed for concentrating light toan elongated absorber including: a trough shaped reflector extendingalong a longitudinal axis, the reflector spaced apart from the absorber.In some embodiments, the reflector has a portion of at least onereflective surface having a shape which substantially corresponds to anedge ray involute of a virtual absorber surrounding the absorber andcontacting the reflector.

In some embodiments, the ratio of the area of the virtual absorber tothe area of the absorber is 0.9 or greater.

In some embodiments, a portion of the reflector at the bottom of thetrough includes a reflective cavity having a reflective surface with ashape that deviates substantially from the edge ray involute of thevirtual absorber.

In some embodiments, the cavity includes a V-shaped trough extendingalong the bottom of the reflector in the direction of the longitudinalaxis.

In some embodiments, the V-shaped trough includes an aperture positionedsuch that the image of the absorber reflected in a wall of the V-shapedtrough has a top which is positioned proximal or above the aperture ofthe V-shaped top in the direction extending from the top of the troughto the bottom of the trough.

Some embodiments are characterized by an efficiency loss averaged overacceptance angle relative to an equivalent gapless concentrator of 0.02or less.

In another aspect, a collector system is disclosed for converting solarlight to heat including: a working fluid; at least one absorber element;and at least one concentrator. In some embodiments, the at least oneconcentrator concentrates solar light onto the absorber element togenerate heat; and the working fluid flows through the absorber elementto extract heat from the absorber element.

In some embodiments the at least one concentrator includes an apparatusof the type described above. In some embodiments, the absorber elementincludes an apparatus of the type described above.

In some embodiments, the system converts solar light to heat with anefficiency of about 30% or greater at an operating temperature of about200 C or greater.

In some embodiments, the system converts solar light to heat with anefficiency of about 40% or greater at an operating temperature of about200 C or greater.

In some embodiments, the system converts solar light to heat with anefficiency of about 45% or greater at an operating temperature of about200 C or greater.

In some embodiments, the system converts solar light to heat with anefficiency of about 50% or greater at an operating temperature of about200 C or greater.

In some embodiments, the system converts solar light to heat with anefficiency of about 30% or greater at an operating temperature of about180 C or greater.

In some embodiments, the system converts solar light to heat with anefficiency of about 40% or greater at an operating temperature of about180 C or greater.

In some embodiments, the system converts solar light to heat with anefficiency of about 45% or greater at an operating temperature of about180 C or greater.

In some embodiments, the system converts solar light to heat with anefficiency of about 50% or greater at an operating temperature of about180 C or greater.

In some embodiments, the system is characterized by an angularacceptance of at least 35 degrees.

In some embodiments, the system is characterized by an angularacceptance of at least 45 degrees.

In some embodiments, the system is characterized by an angularacceptance of at least 60 degrees.

In another aspect, a method is disclosed of converting solar light toheat including: using an apparatus of the type described above,concentrating light onto an absorber to generate heat.

In another aspect, a method is disclosed of converting solar light toheat including: receiving solar light with an apparatus of the typedescribed above to generate heat.

In another aspect, a method is disclosed of converting solar light toheat including: receiving solar light with a system of the typedescribed above to generate heat.

Various embodiments may include any of the above described features,either alone, or in combination.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings are not intended to be drawn to scale. In thedrawings, each identical or nearly identical component that isillustrated in various figures is represented by a like numeral. Forpurposes of clarity, not every component may be labeled in everydrawing. In the drawings:

FIG. 1 is an illustration of the solar geometry.

FIG. 2 is an illustration of a system for converting solar light intoanother form of energy.

FIG. 3A is a side view of a concentrator assembly.

FIG. 3B is a perspective view of a concentrator assembly.

FIG. 4A is a top view of a concentrator assembly.

FIG. 4B is a side view of a concentrator assembly.

FIG. 4C is a cross section of an absorber used in the concentratorassembly of FIGS. 4A-4B.

FIG. 4D illustrates an absorber used in the concentrator assembly ofFIGS. 4A-4B, where the absorber has a cross section of a square.

FIG. 5A is a top view of a concentrator assembly.

FIG. 5B is a side view of a concentrator assembly.

FIG. 5C is a cross section taken transverse the longitudinal axis of anabsorber used in the concentrator assembly of FIGS. 5A-5B.

FIG. 5D is a cross section taken through the longitudinal axis of anabsorber used in the concentrator assembly of FIGS. 5A-5B.

FIG. 6A is a top view of a concentrator assembly.

FIG. 6B is a side view of a concentrator assembly.

FIG. 6C is a cross section taken transverse the longitudinal axis of anabsorber used in the concentrator assembly of FIGS. 6A-6B.

FIG. 6D is a cross section taken through the longitudinal axis of anabsorber used in the concentrator assembly of FIGS. 6A-6B.

FIG. 6E is a perspective view of an absorber used in the concentratorassembly of FIGS. 6A-6B.

FIG. 7A is an illustration of a cross-section of a concentrator assemblyof a first embodiment.

FIG. 7B is an illustration of a cross-section of a concentrator assemblyof a second embodiment.

FIGS. 8A-8E are ray traces of the concentrator assembly of FIG. 7 forrays incident at a variety of angles ranging from −35 degrees to +35degrees.

FIGS. 9A-9B are illustrations of exemplary reflective surfaces for aconcentrator assembly.

FIGS. 10A-10B show plots of collector efficiency versus inlettemperature under a variety of conditions.

FIGS. 11A-11B show plots of collector efficiency versus inlettemperature under a variety of conditions.

FIG. 11C shows a plot of collector efficiency versus inlet temperatureunder a variety of conditions for several types of collectors.

FIG. 12 is a plot of relative efficiency versus angle of incidence ofsolar light for an exemplary concentrator assembly.

FIG. 13 is an illustration of a concentrator design method.

FIGS. 14A and 14B illustrate the use of virtual absorbers in aconcentrator design method.

FIGS. 15A and 15B illustrate a concentrator assembly featuring anabsorber/concentrator gap, and a design method therefore.

FIG. 16 is a plot of the ratio of virtual absorber area to absorber areavs. gap loss for a concentrator assembly featuring anabsorber/concentrator gap.

FIGS. 17A-20 show several embodiments of an optimal design concentrationschematic.

DETAILED DESCRIPTION OF THE INVENTION

From a thermodynamic viewpoint, the solar geometry may be described indirection cosines, which are the momenta of the light rays. Referring toFIG. 1, the sun over the year occupies a band 101 inside a unit radiuscircle 102 which is ±sin 23.5 deg. This band is nearly Vi the area ofthe circle, from which follows, e.g. as described in detail U.S. Pat.No. 6,467,916 to Roland Winston (incorporated herein by reference in itsentirety), that the maximum theoretical concentration for a troughshaped concentrating reflector using no seasonal adjustments is veryclose to 2.

In some embodiments, this limit may be increased. In cases where thetarget (absorber) is immersed in a refractive material having an indexof refraction (n), this limit is multiplied by n squared because themomentum of a light ray is actually the index of refraction×directioncosine. For example, for n˜1.5 (typical of glass or PMMA) andrestricting the absorber irradiance to 60 deg., the maximumconcentration becomes ˜3. In some embodiments featuring a lowconcentration design which can be switched seasonally between 2positions each year (summer and winter) the limits are multiplied by 2(4-6 concentration). For example, embodiments described herein mayfeature a concentration of about 4 or more.

FIG. 2 shows a system 200 for converting solar light into another formof energy, e.g., heat. A concentrator assembly 201 receives light fromthe sun. One or more concentrators concentrate the incident solar lightonto one or more absorbers, which convert the light to heat. This heatis transferred from the concentrator assembly 201, e.g., using acirculating heat transfer fluid to a heat exchanger 202. The heatexchanger 202 outputs the heat received from the concentrator assembly201. The output heat may be used for any suitable purpose including,e.g., providing building heating, generation of electricity, generationof mechanical power, etc.

FIGS. 3 A and 3B illustrate exemplary embodiments of the concentratorassembly 201. The concentrator assembly 201 includes one or more opticalconcentrators 203. Three concentrators 203 are shown in FIG. 3A, fiveare shown in FIG. 3B, and any other number may be used in otherembodiments. Each concentrator 203 concentrates incident solar lightonto a corresponding absorber 204. The absorber 204 absorbs concentratedsolar light and transforms it to heat.

As shown, the concentrators 203 and absorbers 204 are arranged in alinear array. However, any suitable arrangement may be used. Theconcentrators 203 are trough shaped reflectors having an open top endand tapering to a trough bottom. The inner surface of the trough isreflective, e.g., with a reflectivity to solar light of e.g., 80% ormore, 90% or more, 95% or more, etc. In some embodiments, the reflectivesurface may include a reflective coating, e.g., of the types availablefrom Alanod Solar GmbH of Ennepetal, Germany and ReflecTech, Inc. ofArvada, Colo.

The absorbers 204 are elongated tubular (e.g., cylindrical) elementspositioned at or near the bottom of the trough shaped reflectors. Asshown, each of the concentrators 203 is symmetric about an optical plane(indicated with a dashed line in FIG. 3A). In one embodiment, theconcentrator 203 may include a U shape. In another embodiment, theconcentrator 203 may include any shape known in the art so as toconcentrate an optical amount of energy to a predetermined location. Insome embodiments, a heat transfer working fluid (e.g., water, oil, anorganic fluid, or any other suitable fluid known in the art) flowsthrough the absorbers 204 (e.g., in a series arrangement, in a parallelarrangement, etc.). Heat from the absorbers 204 is transferred to thefluid, which flows out of the concentrator assembly 201 to the heatexchanger 202. The energy preferably is captured and used for apredetermined purpose.

As shown, the concentrators 203 and corresponding absorbers 204 arearranged in a linear array. In some embodiments, the concentrators maybe arranged with a center to center spacing of 1.0 m or less, 0.5 m orless, 0.25 m or less, 0.1 m or less, e.g., in the range of 100-400 mm.In some embodiments, the absorbers 204 may have an outer diameter of 100mm or less, 75 mm or less, 50 mm or less, e.g., in the range of 40-60mm.

As described greater detail below, in some embodiments, concentrators203 concentrate substantially all solar light incident at angles to theoptic plane less than an acceptance angle to the absorber 204. In someembodiments, the concentrator 203 concentrates light incident at anglesless than the acceptance angle with an efficiency at the thermodynamiclimit. In some embodiments, the concentrator 203 concentrates lightincident at angles less than the acceptance angle with a geometricconcentration ratio of C of 1.0 or more, 1.1 or more, 1.25 or more, 1.5or more, 1.75 or more, 1.85 or more, 1.9 or more, 2 or more, etc. Insome embodiments this concentration is provided over the year withouttracking.

FIGS. 4A-4C illustrate an exemplary embodiment of the collector assembly201 featuring absorbers 204 having a counter flow arrangement. As shown,absorbers 204 are cylindrical members having an outer transparentevacuated enclosure 401 (e.g., a glass tube). Located within theenclosure is a tubular absorber fin 403 (e.g., an extruded aluminum orcopper pipe) which absorbs solar light incident through the enclosure401 and transforms the light to heat. The absorber fin 401 may include aselective surface 405 which exhibits a high absorptivity to solar lightand a low emissivity (thereby limiting radiative heat loss). Forexample, in some embodiments, the selective surface 405 may exhibit anabsorptivity of 0.75 or more, 0.9 or more, 0.95 or more, 0.99 or moreetc. (e.g., in the range of 0.9 to 0.99). For example, in someembodiments, the selective surface 405 may exhibit an emissivity of 0.25or less, 0.10 or less, 0.05 or less, 0.025 or less etc. (e.g., in therange of 0.04 to 0.05). In some embodiments, the selective surfaceexhibits these absorptivity and emissivity properties at temperature of100 C or greater, 150 C or greater, 175 C or greater, or 200 C orgreater (e.g., in the range of 150-200 C). In some embodiments, theselective surface comprises an aluminum nitride coating, e.g., sputteredon to the outer (vacuum facing) surface of absorber fin 401. In otherembodiments, any other suitable surface or coating known in the art maybe used.

Absorber fin 403 is disposed about an inner tube 407 (e.g., an extrudedaluminum or copper pipe). Heat transfer working fluid flows in to theinner tube 407 to the end of the tube. The fluid returns from the end ofthe tube through an annular space between the inner tube 407 and theabsorber fin 403 (i.e., in a “counter-flow” arrangement). As the fluidpasses through the absorber 204, the fluid absorbs heat from theabsorber fin 403 and carries the heat away from the absorber 204. Thatis, the fluid enters the absorber at a first temperature, is heatedduring its passage, and is output at a second temperature higher thanthe first temperature.

In some embodiments, absorber fin 403 may be made of glass (or othernon-metallic material) and coated with a selective surface 405. In somesuch embodiments, the absorber fin 403 and the enclosure 401 may bejoined using only glass on glass seals, or may be constructed as anintegral unit. Similarly, inner tube 407 may be made of glass (or othernon-metallic material) allowing for the reduction or elimination ofglass on metal seals and/or allowing absorber 204 to be formed as anintegral or substantially integral unit. In one embodiment, thereflective material may comprise a reflective paint, or a mirroredsurface.

Concentrator assembly 201 includes a plumbing system 409 whichfacilitates the flow of heat transfer fluid through the absorbers 204. Apump 411 pumps fluid along an input plumbing line 412 and into theabsorbers 204. For example, pump 411 may pump the fluid with a mass flowrate of 40 g/s or more, 50 g/s or more, 60 g/s or more, 70 g/s or more,80 g/s or more, e.g., in the range of 40-45 g/s. As described above, thefluid is heated during counter flow action. An output plumbing line 413carries the heated fluid away from concentrator assembly 201, e.g., toheat exchanger 202. The pump 411 may be powered by various means and inone embodiment from the collected heat.

FIGS. 5A-5D illustrate an exemplary embodiment of the collector assembly201 featuring absorbers 204 having an alternative counter flowarrangement. As shown, absorbers 204 are cylindrical members having anouter transparent evacuated enclosure 401 (e.g., a glass tube). Locatedwithin the enclosure is a tubular absorber fin 403 (e.g., an extrudedaluminum or copper pipe) which absorbs solar light incident through theenclosure 401 and transforms the light to heat. The absorber fin 403 mayinclude a selective surface 405 which exhibits a high absorptivity tosolar light and a low emissivity (thereby limiting radiative heat loss).For example, in some embodiments, the selective surface 405 may exhibitan absorptivity of 0.75 or more, 0.9 or more, 0.95 or more, 0.99 or moreetc. (e.g., in the range of 0.9 to 0.99). For example, in someembodiments, the selective surface 405 may exhibit an emissivity of 0.25or less, 0.10 or less, 0.05 or less, 0.025 or less etc. (e.g., in therange of 0.04 to 0.05). In some embodiments, the selective surfaceexhibits these absorptivity and emissivity properties at temperature of100 C or greater, 150 C or greater, 175 C or greater, or 200 C orgreater (e.g., in the range of 150-200 C). In some embodiments, theselective surface comprises an aluminum nitride coating, e.g., sputteredon to the outer (vacuum facing) surface of absorber fin 401. In otherembodiments, any other suitable surface or coating known in the art maybe used.

In contrast to the example shown in FIGS. 4A-4C, in the absorber of thecurrent example absorber fin 403 is not disposed about an inner tube407. Instead, a counter flow heat exchange pipe 501 runs along and is inthermal contact with the inner surface of the absorber fin 403. The heatexchange pipe 501 includes an outer tube 502 closed at one end anddisposed about an inner tube 503. Heat transfer working fluid flows intothe inner tube 503 to the end of the pipe 501. The heat transfer fluidreturns through the annular space between the inner tube 503 and theouter tube 502. As the fluid passes through the absorber 204, the fluidabsorbs heat from the absorber fin 403 and carries the heat away fromthe absorber 204. That is, the fluid enters the absorber at a firsttemperature, is heated during its passage, and is output at a secondtemperature higher than the first temperature. If the direction of flowis reversed, the heat exchange is still useful. Because of the highvacuum, the lowest resistance path for the heat is through the fluid.

Heat exchange pipe 501 may be, e.g., welded or otherwise joined toabsorber fin 403. In some embodiments, one or more portions of heat pipe501 and one or more potions of absorber fin 403 are formed as anintegral unit. In another embodiment, the pipe 501 may be connected by amechanical fastener.

Concentrator assembly 201 includes a plumbing system 409 whichfacilitates the flow of heat transfer fluid through the absorbers 204. Apump 411 pumps fluid along an input plumbing line 412 and into theabsorbers 204. For example, pump 411 may pump the fluid with a mass flowrate of 40 g/s or more, 50 g/s or more, 60 g/s or more, 70 g/s or more,80 g/s or more, e.g., in the range of 40-45 g/s. As described above, thefluid is heated during counter flow action in heat pipe 501. An outputplumbing line 413 carries the heated fluid away from concentratorassembly 201, e.g., to heat exchanger 202.

FIGS. 6A-6E illustrate an exemplary embodiment of collector assembly 201featuring absorbers 204 having a so called U-tube flow arrangement. Asshown, absorbers 204 are cylindrical members having an outer transparentevacuated enclosure 401 (e.g., a glass tube). Located within theenclosure is a tubular absorber fin 403 (e.g., an extruded aluminum orcopper pipe) which absorbs solar light incident through the enclosure401 and transforms the light to heat. The absorber fin 401 may include aselective surface 405 which exhibits a high absorptivity to solar lightand a low emissivity (thereby limiting radiative heat loss). Forexample, in some embodiments, the selective surface 405 may exhibit anabsorptivity of 0.75 or more, 0.9 or more, 0.95 or more, 0.99 or moreetc. (e.g., in the range of 0.9 to 0.99). For example, in someembodiments, the selective surface 405 may exhibit an emissivity of 0.25or less, 0.10 or less, 0.05 or less, 0.025 or less etc. (e.g., in therange of 0.04 to 0.05). In some embodiments, the selective surfaceexhibits these absorptivity and emissivity properties at temperature of100 C or greater, 150 C or greater, 175 C or greater, or 200 C orgreater (e.g., in the range of 150-200 C). In some embodiments, theselective surface comprises an aluminum nitride coating, e.g., sputteredon to the outer (vacuum facing) surface of absorber fin 401. In otherembodiments, any other suitable surface or coating known in the art maybe used.

In contrast to the example shown in FIGS. 4A-4C and FIGS. 5A-4C, in theabsorber of the current example absorber fin 403 is not disposed aboutan inner tube 407 and does not include a counter-flow heat exchange pipe501. Instead, a U-shaped tube 601 runs along and is in thermal contactwith the inner surface of the absorber fin 403. Heat transfer workingfluid flows into the U-shaped tube 601 through an input at a proximalend of the absorber 204. The fluid flows down an input portion of thetube to a distal end of absorber 204. The end of the U-shaped tube 601includes a curve portion which directs the fluid back through an outputportion of the tube to an output located at the proximal end of theabsorber 204.

As the fluid passes through the absorber 204, the fluid absorbs heatfrom the absorber fin 403 and carries the heat away from the absorber204. That is, the fluid enters the absorber at a first temperature, isheated during its passage, and is output at a second temperature higherthan the first temperature. Note that the input portion and outputportion of the U-shaped tube 601 are spaced apart from each other.Preferably, the spacing is optimized. Advantageously, the arrangementreduces or eliminates heat flow from the warmer fluid exiting the tubeto the cooler fluid entering the tube. Accordingly, the efficiency ofthe heat exchange between the absorber 204 and the heat exchange workingfluid is increased, e.g., in comparison to flow configurations featuringa counter-flow type arrangement.

U-shaped tube 601 may be, e.g., welded or otherwise joined to absorberfin 403. In some embodiments, one or more portions of U-shaped tube 601and one or more portions absorber fin 403 are formed as an integralunit, e.g., an integral unit of extruded metal (e.g., aluminum orcopper).

Concentrator assembly 201 includes a plumbing system 409 whichfacilitates the flow of heat transfer fluid through the absorbers 204. Apump 411 pumps fluid along an input plumbing line 412 and into theabsorbers 204. For example, pump 411 may pump the fluid with a mass flowrate of 40 g/s or more, 50 g/s or more, 60 g/s or more, 70 g/s or more,80 g/s or more, e.g., in the range of 40-45 g/s. As described above, thefluid is heated during passage through the U-shaped tube 601. An outputplumbing line 413 carries the heated fluid away from concentratorassembly 201, e.g., to heat exchanger 202.

Although the embodiments shown above feature a direct flow plumbingconfiguration, it is to be understood that other plumbing configurationsknown in the art may be used. For example, in some plumbingconfigurations, pump 411 is omitted, and the flow of the heat transferworking fluid is driven, e.g., by gravity or thermal convection.

FIG. 7A illustrates a cross-section of a concentrator assembly 201 of afirst embodiment. The concentrator assembly 201 illustrated in FIG. 7Ashows a cross section of a trough shaped reflective surface 701 ofconcentrator 203 designed for the absorber fin of FIG. 4. FIG. 7Billustrates a cross-section of a concentrator assembly 201 of a secondembodiment. The concentrator assembly 201 illustrated in FIG. 7B shows across section of a trough shaped reflective surface 701 of concentrator203 may be designed for the absorber fin of FIGS. 5 and 6. Thereflective surface 701 illustrated in FIGS. 7A and 7B extends in and outof the plane of the page along a longitudinal axis. Cylindrical absorber204 is located at the bottom of the trough and also extends along thedirection of the longitudinal axis. The top of the trough forms an inputaperture. The reflective surface is shaped such that substantially alllight rays incident on the input aperture at angles less than anacceptance angle are directed to a surface of absorber 204 (e.g., thesurface of a cylindrical absorber fin 403 of absorber 204). FIGS. 8A-8Eare ray traces of the reflector surface 701 of FIG. 7A, which illustratethe concentration of light at angles less than an acceptance angle of 34degrees. The ray traces of the reflector surface 701 of a differentshape, for example the reflector surface illustrated in FIG. 7B, wouldbe very similar.

The acceptance angle can be designed according to the desiredconcentration factor, the concentrated flux profile and the orientationof the absorber tubes (East-West or North-South, horizontal or tilted,etc.). In one embodiment, the tilt may be determined based on a locationof system. Orienting the absorber tubes North-South (N-S) requireslarger acceptance angles to ensure sufficient illumination throughoutthe day, which reduces the concentration factor. Therefore, an East-West(E-W) orientation is generally advantageous. However, a N-S orientedreflector (with the larger acceptance angle) does accept more diffusesolar irradiation and so too has some positive performance attributes.Additionally, reflectors with larger acceptance angles will generallyrequire less reflector area, which provides an economic advantage. FIGS.9A and 9B show exemplary shapes for the reflective surface 701. In FIG.9A the surface 701 has been optimized for use with a concentrator 204oriented in the N-S direction and has an acceptance angle of 60 degrees.In FIG. 9B the surface 701 has been optimized for use with aconcentrator 204 oriented in the E-W direction, with an acceptance angleof 34 degrees.

FIGS. 10A-10B illustrate plots of collector efficiency versus heatexchange fluid intake temperature for concentrator assemblies 201 invarious configurations. The collector efficiency is defined as the ratioof the useful power extracted from the collector divided by the productof the collected irradiance and the effective aperture area of thecollector (defined as the length of the active area of the absorber tube204, which is the area covered by the selective coating 405, times thewidth of the reflector). Various collector efficiencies may changedepending on one or more parameters and the plot forms no limitations tothe present disclosure.

Plots are shown for concentrator assemblies with absorbers 204 in theU-Tube (e.g., as shown in FIGS. 6A-6E), X-Tube (the X-tube has similarheat exchange properties to the counter flow tube), and counter flow(CF) (e.g., as shown in FIGS. 5A-5D) configurations. In each case, theconcentrator assemblies are in the E-W arrangement. The type ofreflective surface used is indicated (i.e. 92% reflectivity materialavailable from Alanod or 94% reflectivity material available fromReflecTech). In each case the ambient temperature is 25 C, and theincident solar irradiance is G=1000 W/m². FIG. 10A shows efficienciesbased on direct normal incidence (DNI). FIG. 10B shows efficienciesbased on effective irradiance (i.e., the direct irradiance plus thediffuse irradiance divided by the concentration ratio of theconcentrator assembly).

Referring to FIGS. 10A and 10B, at an inlet temperature of 200 C, theU-Tube configuration (with ReflecTech and Alanod reflective surfaces)provides the highest collector efficiency of about 45% or more. At aninlet temperature of 200 C, the X-Tube and CF configurations providesimilar collector efficiency in comparison to each other, but inferiorefficiency compared to the U-Tube configuration. However, for inlettemperatures in the range of 40 C to 140 C, the X-Tube configurationprovides the best performance of any configuration.

FIGS. 11A and 11B are plots of collector efficiency versus heat exchangefluid intake temperature for concentrator assemblies 201 in variousconfigurations. The collector efficiency is defined as the ratio of theuseful power extracted from the collector divided by the product of thecollected irradiance and the effective aperture area of the collector(defined as the length of the active area of the absorber tube 204,which is the area covered by the selective coating 405, times the widthof the reflector).

Plots are shown for concentrator assemblies with absorbers 204 in theU-Tube (e.g., as shown in FIGS. 6A-6E) configuration for both E-W andN-S arrangement. The type of reflective surface used is indicated (i.e.92% reflectivity material available from Alanod or 94% reflectivitymaterial available from ReflecTech). In each case the ambienttemperature is 25 C, and the incident solar irradiance is G=1000 W/m².FIG. 11A shows efficiencies based on direct normal incidence (DNI). FIG.11B shows efficiencies based on effective irradiance (i.e., the directirradiance plus the diffuse irradiance divided by the concentrationratio of the concentrator assembly).

Referring to FIGS. 11A and 11B, at an inlet temperature of 200 C, theU-Tube configuration (with ReflecTech and Alanod reflective surfaces)with E-W arrangement provides the highest collector efficiency of about45% or more. At 200 C, the N-S arrangement provides inferior efficiencycompared to E-W. However, for inlet temperatures in the range of 40 C to140 C, the N-S arrangement provides better performance than the E-Warrangement.

FIG. 11C shows plots of collector efficiency versus operatingtemperature (mean temperature above ambient) for concentrator assemblies201 in comparison to collector efficiencies of other types of collectorsknown in the art. The collector efficiency is defined as the ratio ofthe useful power extracted from the collector divided by the product ofthe collected DNI irradiance and the effective aperture area of thecollector. In each case the ambient temperature is 25 C, and theincident solar irradiance is G=800 W/m². The concentration ratio foreach collector type is indicated.

Plots are shown for concentrator assemblies with absorbers 204 in theU-Tube (e.g., as shown in FIGS. 6A-6E) configuration for both E-W andN-S arrangement. Plots are also shown for three non-tracking collectors:a flat plate solar collector, an Apricus evacuated heat pipe collector,and a Winston/Bergquam collector featuring an evacuated tube having aninternally located non-imaging (compound parabolic concentrator)collector. Plots are also shown for two tracking collectors: a Chromasunlinear Fresnel mirror collector and a Sopogy parabolic trough collector.

Referring to FIG. 11C, note that at temperatures near 200 C, the U-TubeE-W concentrator outperforms all other collectors (tracking ornon-tracking). Further at temperatures in the range of 100-200 C, theU-Tube E-W and U-Tube N-S concentrators perform much better than thenon-tracking flat plate and Apricus collectors, and comparable to orbetter than the remaining collectors.

FIG. 12 shows a plot of the relative efficiency of a collector featuringan E-W oriented absorber in the U-tube configuration as a function ofthe angle of incident solar radiation. Note that the relative efficiencyis substantially constant at about 100% over angles less than the 35degree acceptance angle of the concentrator 203 designed for E-W.

In the examples described above, it is advantageous if the reflectivesurface 701 of the concentrators 203 has a shape which ensures that allor substantially all (e.g., in the absence of losses such as those dueto imperfect reflectivity) light rays incident on the concentrator 203at angles less than an acceptance angle are concentrated to an absorber.This condition provides for efficient use of the absorber 204, which, inmany applications is a costly component, e.g., with a cost thatincreases with size.

In some embodiments, the shape of the reflective surface 701 may bedetermined by considering the active surface of absorber 204 (e.g.,selective surface 405) to be a light emitting surface and requiring thatthe reflective surface 701 be shaped such that no light rays emanatingfrom the surface of absorber 204 return to the absorber 204. In theterminology of radiation transfer, the view factor from absorber back toitself is zero. It follows from energy conservation that light startingfrom the emitting surface will (after zero, one or more reflections)invariably reach the sky. The shape factor is one. Note, that in thisdiscussion, it is understood that material losses, like imperfectreflectivity are not included. In one embodiment, the radiation shapefactor from the desired phase space of the sky is also at maximum, theshape factor from desired phase space of sky to light emitting surfaceis also one. In special cases, both shape factors can be one, giving aclass of non-imaging optical concentrators described. However, in mostcases this is not practical and a compromise solution is sought. Thefollowing describes methods for ensuring the shape factor from theabsorber is one, which is frequently the option. The following alsodescribes techniques for obtaining improved or optimal designs whichtake into account practical considerations for real absorbers, e.g.,concentrator/absorber gaps. For example, the shape may compriseinvolutes of a circle arc. For example, the shape may also compriseparabolic shape for the concentrator.

For example, FIG. 13 illustrates a method of designing a concentrator203 for a cylindrical absorber 204 in which the shape factor from theabsorber is one. Here, the active surface of the absorber is taken to bethe outer surface of the cylinder. The reflective surface 701 of theconcentrator 203 includes two symmetrically disposed edge ray involutes1301 of the cylinder.

As used herein, an edge ray involute of an absorber is a curve 1301determined using the following procedure. A taut string is considered tobe wrapped around the absorber 204. While maintaining the string tautand holding its length constant, an end 1305 of the string is unwrappeduntil the string is tangent to the surface of the absorber 204. The pathof the end of the string defines a first portion 1309 of the edge rayinvolute 1301. At this point, the edge ray involute is equivalent to thestandard involute familiar from differential geometry (see, e.g.,http://mathworld.wolfram.com/Involute.html).

Next, to define a second portion 1308 of the edge ray involute 1301, thestring is extended to include a second line segment 1304 extending fromthe end of the first line segment 1302 to an end 1307 which normallyintersects (i.e. intersects at right angles to) a line 1303. The edgeline 1303 extends from an edge 1311 of the entrance aperture 1310 of theconcentrator 203 at an angle corresponding to the acceptance angle ofthe concentrator 203. The edge line 1303 corresponds to the wave frontof an edge ray of the concentrator 203 (i.e., the light ray 1312incident with the maximum acceptance angle of the concentrator).

The extended string has the form of a taut string, which extends arounda curve point 1313 placed at the end of the first line segment 1302 tothe edge line 1303. The end 1307 of the string is allowed to slidefrictionlessly along the edge line 1303 while maintaining the normalorientation of second line segment 1304 to the edge line 1303. Thus, asthe end 1307 slides with the string kept taut, the position of the curvepoint 1313 is adjusted to maintain the normal orientation of second linesegment 1304 to edge line 1303. The path of curve point 1313 continuesto trace out the remaining portion of the edge ray involute.

As the slope of the involute defined by the movement of the curve point1313 increase towards infinity, the process is stopped, and one half ofthe reflective surface 701 of concentrator 203 has been defined. Theremainder of the surface may be obtained by reflection in the opticplane of the concentrator 203. Alternatively, the process may be endedbefore the slope approaches infinity to produce a truncated design(e.g., in cases where material costs, weight, or other considerationspreclude full extension of the reflective surface).

Not wishing to be bound by theory, using the framework of the Hottelstring method familiar from thermodynamics (see, e.g., Hoyt C. Hottel,Radiant-Heat Transmission 1954, Chapter 4 in William H. McAdams (ed.),Heat Transmission, 3rd ed. McGraw-Hill), which is herein incorporated byreference in its entirety, it can be shown that the above describedstring-based design method will result in a concentrator design whichoperates at the thermodynamic limit. As will be apparent to one skilledin the art, the method may be easily adapted to absorbers having othercross sectional shapes, including square shapes, round shapes, irregularshapes, etc. Further, the design method may be used, in some cases, forexample flat absorbers to obtain three dimensional concentrators byrotation of the two dimensional solution about the optic axis. FIG. 4Dillustrates an exemplary embodiment of an absorber with an outertransparent evacuated enclosure and inner absorber fin with across-section of a square. The absorber illustrated in FIG. 4D may beused in the concentrator assembly of FIGS. 4A-4B.

The design method described above may be implemented as software on acomputer. The output of the design method software may be, e.g., a datafile, an image, a print out, etc. The output of the design methodsoftware may control one or more automated fabrication tools tofabricate a concentrator. The designs may be evaluated and/or optimizedusing optical design tools, e.g., including ray tracing applications andother optical design applications know in the art.

The string method described above will necessarily result in a designwhere the active surface of the absorber 204 is in contact with thereflective surface 701 of the concentrator 203 at one or more points. Inpractice, it may be impossible to meet this condition. For example, asdescribed above, the active surface of an absorber 204 may be aselective surface 405 located within an evacuated enclosure 401. Thepresence of the enclosure 401 requires a gap between the selectivesurface 405 and the reflective surface 701 of the concentrator 203. Sucha gap will result in a design which does not operate at thethermodynamic limit (i.e., the shape factor from the active surface ofthe absorber 204 may be less than one or some light incident on theconcentrator may miss the absorber).

The following presents techniques for providing advantageousconcentrator designs which take into account an absorber/concentratorgap. Consider a linear (2-D) non-imaging concentrator. In the absence ofdielectric materials (no refraction) the angular acceptance is anellipse in direction cosines with semi axes sin(θ₀) and 1. For thecurrent model, this phase space ellipse is considered uniformlypopulated in a Lambertian sense. Then the maximum flux concentrationC_(o) is 1/sin(θ₀) and the maximum irradiance on the absorber isI₀/sin(θ₀) (all material losses, etc are neglected). I₀ is theirradiance on the aperture.

As noted above, idealized designs have no geometrical losses, thereflectors touch the absorber, one simply chooses C˜C₀ (or less, e.g.,to save material via truncation) and the design is determined. But in apractical design, the reflector cannot touch the absorber (resulting ina gap) and C is not necessarily ˜C₀, it can be smaller or larger. Thefollowing describes a method of making design choices which result in anadvantageous concentrator design even in the presence of aconcentrator/absorber gap.

Solar collector performance can be modeled as:Q _(out)=η₀ Q _(in) −Q _(loss)

where η₀ is the optical efficiency, Q_(in) is the insolation (I)multiplied by the aperture area (A) and Q_(loss) is a function of T(absorber temperature), T_(A) (ambient temperature) and perhaps someother factors. For evacuated receivers, Q_(loss) is to an excellentapproximation A_(abs) εσ(T⁴−T_(A) ⁴) where A_(abs) is the absorber area,c is the emissivity and σ=5.67×10⁻⁸ in MKS units. Then the operatingefficiencyη=Q _(out) /Q _(in)=η₀ −Q _(loss) /Q _(in)=η₀ −[A _(abs) /A]f(T,T_(A))/I

Since A/A_(abs)=C, the

-   -   geometrical    -   concentration        η=η₀−[1/C]f(T,T _(A))/I.

Accordingly, the design procedure involves maximizing η by appropriatelyselecting η₀ and C. Several approaches are available for accommodating agap between absorber and reflector. Referring to FIG. 14A, one approachis to surround the physical absorber 204 by a virtual absorber 1401which contacts the reflective surface 701 of the concentrator 203. Thevirtual absorber 1401 has virtual absorber area A′_(abs). Then η₀rescales asη₀′=(A _(abs) /A′ _(abs))η₀as follows from reciprocity and the view factor from A_(abs) toA′_(abs)=1. Designing forA′ _(abs) /A=sin(θ)=1/C ₀ while A _(abs) /A=1/C givesη=η_(0 ′−[)1/C]f (T,T _(A))/I=(A _(abs) /A′ _(abs))η₀−(A _(abs) /A)f(T,TA)/I=(C)η₀−(A _(abs) /A′ _(abs))(A′ _(abs) /A)f(T,T _(A))/I=(A _(abs) /A′ _(abs))η₀−(A _(abs) /A′ _(abs))(1/C)f(T,T _(A))/I=(A _(abs) /A′ _(abs))[η₀−(sin(θ)f(T,T _(A))/I].

Note C has been replaced by 1/sin (θ). Note that, in practice there isusually some truncation to save reflector material, so C may be less.

Accordingly, a reflector design may be optimized by makingA′_(abs)/A_(abs) approach 1 , e.g., as shown in FIG. 14B. Once thisoptimum virtual absorber shape has been determined, the shape of theconcentrator may be obtained, e.g., using the string method describedabove with the virtual absorber 1401 in place of the actual absorber204.

Note thatQ _(out) =Aη=(CA _(abs))[η₀−(sin(θ)f(T,T _(A))/I]=[A _(abs)/sin(θ)][η₀−(sin(θ)f(T,T _(A))/I]is independent of A′_(abs). That is, the absorber has the maximumirradiance allowed by thermodynamics (second law). For additionalbackground on the use of virtual absorbers in concentrator design, seeR. Winston, Ideal Flux Concentrators with Reflector Gaps, Applied Optics17, 1668 (1978), which is incorporated by reference in its entirety.

Another approach to dealing with a concentrator/absorber gap is toimmerse the absorber in a cavity. See, e.g., R. Winston, CavityEnhancement by Controlled Directional Scattering, Appl. Opt. 19, 195(1980), which is incorporated by reference in its entirety.

In this case η₀ is essentially unchanged, but C is significantlyreduced. This gives η=η₀ −[1/C]f(T, T_(A))/I and there is thepossibility of trading off η₀ against C. In other words, one can onlypartially immerse the absorber in the cavity, thereby incurring someloss, but restore some of the lost C in the concentrator design. Thistradeoff is temperature dependent; and typically it is more advantageousto increase C when the temperature is high.

The cavity design may take a variety of forms, e.g., single or multipleV-shaped grooves or W-shaped grooves. There is a natural upper bound forthe groove design in a cylindrical absorber, where the gap distancebetween the absorber and the concentrator is equal to the radius of theabsorber. In the trade-off between concentration and gap loss, theengineering optimum is neither extreme but rather some intermediatechoice between a fully cavity immersed absorber, and no cavity at all(i.e., a design based on the virtual absorber technique describedabove). As shown in FIG. 16, in typical embodiments the concentrationincreases linearly with gap size, but the gap loss only increasesquadratically, thereby favoring partial immersion. Note the gap losscalculated by our thermodynamic (string) method is the average over theacceptance angle. The loss at a particular angle may vary and istypically greatest at zero angle, and substantially zero near the angleof acceptance.

For example, referring to FIG. 15A, trough shaped concentrator 203features a V-shaped cavity portion 1501 running along the bottom of thetrough and providing partial immersion of the cylindrical absorber 204.The shape of the remaining portion 1502 of the trough is determined,e.g., using the virtual absorber and string method described above. Asshown, the design is characterized by a virtual to physical absorberratio of A′_(abs)/A_(abs)=0.92 and a gap loss of 0.01.

Appendix 1 includes an exemplary algorithm script written in the wellknown Scilab scientific computing environment (available at“http://www.scilab.org”) for designing a concentrator of the typedescribed above. As will be understood by those skilled in the art, thisparticular exemplary algorithm may be modified or extended based onparticular design requirements.

In other embodiments, other suitable values for A′_(abs)/A_(abs) and gaploss may be chosen. In general, once these values are selected, one isstill left with the choice of cavity parameters, e.g., choosing thecoordinates of the V-shaped cavity aperture and the opening half angle αof the V. In some embodiments, a large opening angle (i.e. a shallow V)is favorable to minimize material used.

The following describes an exemplary method for determining the cavityparameters. Referring to FIG. 15B, a cylindrical absorber 204 of radiusr is centered at the origin. One locates the center (O_(x), O_(y)) ofthe image 1504 of the cylindrical absorber which would be formed if thereflective V-shaped cavity is extended as shown (indicated with a dottedline), so that the top of the image circle is even with or slightlyabove the aperture of the cavity. Based on this requirement, the endpoints of the cavity aperture may be determined. For example, a Scilabscript shown in Appendix 1 may be used to determine the position of theend points in an exemplary embodiment. Here, the end points are atcoordinates x=+/−0.48, y=−1.25. The final step in determining the cavityparameters is to determine y_(min). The opening half angle α of theV-shaped cavity and y_(min) are related by tan (α)=x/(y−y_(min)).Further, it can be shown that O_(y)=2 y_(min) sin²α.

Based on these relations, one can calculate a table of possible valuesof y_(min), α, O_(y), (y−O_(y)) and compare with r to find a reasonablesolution. Table 1 below is an exemplary table of values for the designshown in FIGS. 15A-15B. In this case, with r=1.05, one sees thaty_(min)=−1.52 is a reasonable choice.

TABLE 1 y_(min) α O_(y) (y-O_(y)) −1.6 53.7 −2.08 −0.83 −1.54 58.8 −2.25−1.10 −1.53 59.6 −2.28 −1.03 −1.52 60.5 −2.30 −1.05 −1.50 62.3 −2.35−1.30 −1.40 72.6 −2.55 −1.30Although the specific examples described above have dealt withconcentrating radiation to an absorber to generate heat, it is to beunderstood that in various embodiments the absorber may be a transducerwhich converts solar light to another form of energy. For example, theabsorber may include photovoltaic material which generates electricityin response to incident light. In some embodiments, the absorber maytransform incident light into multiple different forms of energy, e.g.,electricity and heat. For example, U.S. Provisional Patent Ser. No.61/378,301, filed Aug. 30, 2010, the entire contents of which areincorporated herein by reference, describes absorbers which include PVmaterial and selective thermal absorbers.

In contrast to conventional optical design, the solar concentrators ofthis disclosure are designed from the principles of thermodynamics, andin particular the second law. TdS=dE+PdV is arguably the most importantequation in Science. If we were asked to predict what currently acceptedprinciple would be valid 1,000 years from now, the Second Law ofthermodynamics would be a good bet. From this we can derive entropicforces: F=T grad S, The Stefan-Boltzmann radiation law (const. T⁴),Information theory (Shannon, Gabor), Accelerated expansion of theUniverse, and even Gravity. We can illustrate the Failure ofconventional optics by a thought experiment; small bodies A, B at fociof an ellipse as shown in FIG. 17A. A portion of the ellipse is replacedby a sphere centered at A.

It appears that FAB<<FBA where FAB is the probability of radiationstarting at A reaching B—etc so A would heat up at the expense of Bcooling down, but that violates the second law.

To understand these things it is best to start with the theory offurnaces. We start with a three wall furnace shown in FIG. 17B. Fij areprobabilities of radiation from wall i reaching wall j. As there are 6unknown Fij, six equations are needed. Three come from energyconservation, and 3 from the second law. The results follow readily frominspection.F12=(A1+A2−A3)/(2A1)F13=(A1+A3−A2)/(2A1)F23=(A2+A3−A1)/(2A2)

where A1, A2, A3 are the three sides shown in FIG. 17B.

FIG. 17C shows a 4-wall enclosure, which is a configuration of greaterinterest. The 4-wall enclosure readily reduces to two 3-wall enclosuresso that we can apply the above formula.F14=[(A5+A6)−(A2+A3)]/(2A1)F23=[(A5+A6)−(A1+A4)]/(2A2).

Turning to FIG. 17D, there is shown a schematic view of a radiationsource 1700, an aperture 1702 and an absorber 1704 that includes ageneral convex or flat shape. A number of parameters of the absorber andaperture will be shown and now explained for optimal operation and formanufacturing. The present disclosure includes a convex or flat shapethat provides a high probability that the solar radiation willconcentrate at a preselected portion to capture as much solar radiationas possible. As can be seen a number of relationships are establishedbetween the radiation source, the aperture and the absorber as shown by1, 2, 3. Suppose the radiation source 1 (example the sun) is maintainedat temperature T1. Then the temperature of the absorber 3 will reach T1if and only if F31=1.

Proof: q13=σT1*⁴A1F13=σT1*⁴A3F31, where qij is the radiation transferfrom i to j.

But q3total=σT3*⁴A3≥q13 at steady state.T3≤T1(second law)→F31=1 if and only if T3=T1.

The first law of thermodynamics (energy conservation) allows q12=q13which implies F12=F13 for a maximally efficient concentrator. Define thegeometric concentration C=A2/A3. The second law requires A1F13=A3F31.Then F12=F13 implies A1F12=A3F31. This implies A3F31 is constantindependent of the optical design. C is maximum when A3 is minimum whichimplies F31 is maximum=1. Again we find that the combination of maximumconcentration and maximum efficiency requires F31=1. We can think ofthis as maximum thermodynamic efficiency. F31=1 also provides animportant relation for concentration because A3=A1F12 but A1F12=A2F21 bythe second law. It follows that Cmax=1/F21 which expresses maximumconcentration as the reciprocal of the probability that radiation fromthe concentrator aperture (A2) regarded as a black body would reach thesource A1.

An important case is the source 1 at ∞ (example very far away, like thesun). Suppose we wish to efficiently concentrate energy from a range ofsun angles+/−Θ, for example, a range of angles sufficient tosubstantially include the solar angles during the year so that trackingis not needed. Mathematically the measure of far away is set by thedimension of A2 (L2) so that far means d>>L2, where d is the distancebetween 1 and 2. As d approaches ∞ the strings become parallel.Long String−Short string=S1−S2=L2 sinΘ.

F21 approaches sin Θ.

Notice Θ is the maximum angle of radiation incident on A2. Cmax=1/sin Θ.

As the distance approaches infinity, the sun's rays appear almostparallel to one another. Therefore, as we approach infinity, F21 isequal to sin Θ, where Θ is equal to the angle of the essentiallyparallel sun's rays at one sun angle with respect to the axis as shownin FIG. 18. Therefore, Cmax=1/sin Θ and note that in this embodiment,the maximum angle on A2 is Θ. For three dimensions,F21=(S1−S2² /L2²),

where L2 is the diameter of A2. As we approach infinity, F21 is equal tosine Θ².

Therefore Cmax=1/sin² Θ, another example of the principle that maximumconcentration is the reciprocal of the probability that radiation fromthe concentrator aperture regarded as a black body would reach thesource.

Another way to obtain the sine law is to consider the angular momentumwith respect to the axis of symmetry shown in FIG. 20. The opticalmomentum is P=n(L, M, N), where n is the index of refraction and L, M, Nare the direction cosines of the rays and the maximum angular momentumat the entrance A2 of the concentrator is J=(L2/2) sin Θ, and at theexit A3 the maximum value of J is L3/2, where L3 is the diameter of A3.Since J is conserved, the maximum concentration is (L2/L3)²=1/sin^(e) Θ.For simplicity we have assumed n=1 in this example.

In another embodiment of the present disclosure, the present inventionmay be used in a water desalination and purification plant that removessalt from various types of water sources including sea water, brackishwater etc. with the objective of providing fresh water for every dayconsumer use. There are two main types of desalination technologies thatare most prevalent today. The most common are various distillationprocesses that require high temperatures for operation. The second typeis reverse osmosis, which requires high pressure to drive pure waterthrough a membrane separation process. Water purification focuses moreon the removal of various particulate, organic and inorganic impuritiesfrom existing fresh water supplies or when attempting to implement waterreclamation projects.

In another embodiment of the present disclosure, the solar array mayinclude a reflective surface that is a Compound Parabolic Concentrator(CPC). For example, the reflective surface may include a two dimensioncompact parabolic concentrator that is an ideal concentrator, i.e., itworks perfectly for all rays within the acceptance angle q, and rotatingthe profile about the axis of symmetry gives the 3-D CPC. The 3-D CPC isvery close to ideal reflective surface.

In another embodiment of the present disclosure, the solar array mayalso include Collimator for a Tubular Light Source. The collimator mayinclude a predetermined shape on each side of the tubular light sourceto collect the light in a predetermined location as discussed.

Although the specific examples described above have dealt withconcentrating radiation from a relatively large solid angle of incidenceonto a relatively small target (e.g. concentrating solar light onto anabsorber), it will be understood that they may equally well be appliedto broadcasting radiation from a relatively small source to a relativelylarge solid angle (e.g. collecting light from an LED chip to form a beamor sheet of light). The small source may, for example, include a lightemitting diode, an organic light emitting diode, a laser, or a lamp.

Although a number of exemplary light concentrators have been described,in various embodiments, any other suitable concentrator may be used. Forexample, in some embodiments, non-imaging concentrators of the typedescribed in Roland Winston et al, Nonimaging Optics, Academic Press(Elsevier, 2005) may be used, including concentrator designed using theedge ray principle as described therein. In various embodimentsconcentrators may include reflective, refraction, diffractive or otherelements. In some embodiments, at least a portion of the concentratormay reflect light by total internal reflection.

One or more or any part thereof of the techniques described herein canbe implemented in computer hardware or software, or a combination ofboth. The methods can be implemented in computer programs using standardprogramming techniques following the method and figures describedherein. Program code is applied to input data to perform the functionsdescribed herein and generate output information. The output informationis applied to one or more output devices such as a display monitor. Eachprogram may be implemented in a high level procedural or object orientedprogramming language to communicate with a computer system. However, theprograms can be implemented in assembly or machine language, if desired.In any case, the language can be a compiled or interpreted language.Moreover, the program can run on dedicated integrated circuitspreprogrammed for that purpose.

Each such computer program is preferably stored on a storage medium ordevice (e.g., ROM or magnetic diskette) readable by a general or specialpurpose programmable computer, for configuring and operating thecomputer when the storage media or device is read by the computer toperform the procedures described herein. The computer program can alsoreside in cache or main memory during program execution. The analysismethod can also be implemented as a computer-readable storage medium,configured with a computer program, where the storage medium soconfigured causes a computer to operate in a specific and predefinedmanner to perform the functions described herein.

A number of embodiments of the invention have been described.Nevertheless, it will be understood that various modifications may bemade without departing from the spirit and scope of the invention.

As used herein the term “light” and related terms (e.g. “optical”) areto be understood to include electromagnetic radiation both within andoutside of the visible spectrum, including, for example, ultraviolet andinfrared radiation.

As will be understood by one skilled in the art, for any and allpurposes, particularly in terms of providing a written description, allranges disclosed herein also encompass any and all possible subrangesand combinations of subranges thereof. Any listed range can be easilyrecognized as sufficiently describing and enabling the same range beingbroken down into at least equal halves, thirds, quarters, fifths,tenths, etc. As a non-limiting example, each range discussed herein canbe readily broken down into a lower third, middle third and upper third,etc. As will also be understood by one skilled in the art all languagesuch as “up to,” “at least,” “greater than,” “less than,” and the likeinclude the number recited and refer to ranges which can be subsequentlybroken down into subranges as discussed above.

Definitions that are contained in text incorporated by reference areexcluded to the extent that they contradict definitions in thisdisclosure. For the purposes of this disclosure and unless otherwisespecified, “a” or “an” means “one or more.”

As used herein, the term “comprising” is intended to mean that thecompositions and methods include the recited elements, but not excludingothers. “Consisting essentially of” when used to define compositions andmethods, shall mean excluding other elements of any essentialsignificance to the combination for that intended purpose. “Consistingof” shall mean excluding more than trace elements of other ingredientsand substantial method steps for making or using the concentrators orarticles of this invention.

The construction and arrangements of the solar energy concentrator, asshown in the various exemplary embodiments, are illustrative only.Although only a few embodiments have been described in detail in thisdisclosure, many modifications are possible (example, variations insizes, dimensions, structures, shapes and proportions of the variouselements, values of parameters, mounting arrangements, use of materials,colors, orientations, etc.) without materially departing from the novelteachings and advantages of the subject matter described herein. Someelements shown as integrally formed may be constructed of multiple partsor elements, the position of elements may be reversed or otherwisevaried, and the nature or number of discrete elements or positions maybe altered or varied. The order or sequence of any process, logicalalgorithm, or method steps may be varied or re-sequenced according toalternative embodiments. Other substitutions, modifications, changes andomissions may also be made in the design, operating conditions andarrangement of the various exemplary embodiments without departing fromthe scope of the present disclosure.

Having thus described several aspects of at least one embodiment of thisinvention, it is to be appreciated various alterations, modifications,and improvements will readily occur to those skilled in the art. Suchalterations, modifications, and improvements are intended to be part ofthis disclosure, and are intended to be within the spirit and scope ofthe invention. Accordingly, the foregoing description and drawings areby way of example only.

APPENDIX I %Mind the Gap Version 2 N0=1000; N1=100; N2=1000; %Defineparameters R=1.05; %10.5mm R1=1.35; % 13.5mm D1=2.7; %27mmtheta=(2*pi/360)*(40); %40deg phi=(2*pi/360)* 14; %14degpsi=(pi/2)+theta; scale=1.0; %---------------------------------------------------------------------------------L1 =scale*pi*R* (1/(sin(theta){circumflex over( )}2)+((cot(theta)){circumflex over( )}2)*(1/(sin(theta))+1){circumflex over ( )}2){circumflex over( )}(1/2); inc=(L 1 +3 * R)/N2; L=(5*R*pi/2)+(R*(theta−2*phi))+L1; %---------------------------------------------------------------------------------x0=R*sin(psi)−L1 *sin(theta); y0=−R*cos(psi)+L1 *cos(theta); %---------------------------------------------------------------------------------%profile for involution gamma=(psi−phi)/N1; sl=(psi−phi)*R;xi(1)=R*cos(theta)+s1*sin(theta); yi(1)=R* sin(theta)−s1*cos(theta);xl(1)=−xi(1); rho(1)=sqrt(xi(1){circumflex over ( )}2+yi(1){circumflexover ( )}2); n=1; while (rho>=R1); sn=s1 −R*((n−1)*gamma);xi(n)=R*cos(theta−(n−1)*gamma)+sn*sin(theta−(n−1)*gamma); yi(n)=R*sin(theta−(n−1)*gamma)−sn*cos(theta−(n−1)*gamma); xl(n)=−xi(n);rho=sqrt(xi(n){circumflex over ( )}2+yi(n){circumflex over ( )}2) n=n+1%vee a=−xi(n−1); b=yi(n−1); end; %Vee c=−1.54; %ymin x6(1)=−a y6(1)=bx6(2)=0; y6(2)=c; x6(3)=a; y6(3)=b;%--------------------------------------------------------- %profile forone reflection flag=0; i=0; s=(2*cos(theta)/N0)*(L1*sin(theta)−R*sin(psi));%--------------------------------------------------------- for n=1:N0;i=0; flag=0; xn=((n−1)*s)/cos(theta)+x0; Lt=L−((n−1)*s*tan(theta)); %---------------------------------------------------- while(flag==0)i=i+1; sL=i*inc; xtn=sL*sin(theta)+xn; ytn=y0−sL*cos(theta); %---------------------------------------------------- Rt=(xtn{circumflexover ( )}2+ytn{circumflex over ( )}2){circumflex over ( )}(1/2);beta1=asin(ytn/Rt); beta2=acos(R/Rt); %----------------------------------------------------alpha=(3*pi/2)−(beta1+beta2); Lt2=sL+(xtn{circumflex over( )}2+ytn{circumflex over ( )}2−R{circumflex over ( )}2){circumflex over( )}(1/2)+R* alpha; if((Lt2>=Lt)&(flag==0)) flag=1; x(n)=xtn; y(n)=ytn;x2(n)=−xtn; end; end; end; d=8.5; %85mm xt(1)=x(1); yt(1)=y(1);xtl(1)=−xt(1); n=1; while (x(n)<=d/2) xt(n)=x(n); yt(n)=y(n);xtl(n)=−x(n); n=n+1; end;%------------------------------------------------------------------------------------%absorber circle profile for j=1:100; angle=(j−1)*2*pi/100;x3(j)=R*cos(angle); y3(j)=R* sin(angle); end;%--------------------------------------------- %Output valuesplot(xi,yi,x1,yi,xt,yt,xt1,yt,x3,y3,x6,y6); axis equal; grid;title(‘theta=40deg, phi=14deg, R=1.05cm, R1=1.35cm,ymin=−1.54cm,d=8.5cm’); c,xi,yi,xt,yt print,====================================================== %maximizes CPCwith gap %r2=r1+gap %Cmax=1/sin(theta); %x=C/Cmax; %y=gap Loss*(C/Cmax); r1=1.05; r2=1.35; z=r2/r1; alf=acos(r1/r2);bet=sqrt(z*z−1)−alf; fi=asin(r1/r2); psimin=fi;xmin=(psimin+fi+1/tan(fi))/pi; xmax=1+bet/pi; for i=1:10; x(i)=xmin+i*(xmax−xmin)/10; psi=pi *x(i)−(fi+1/tan(fi));y(i)=(fi+1/tan(fi))−(psi+cos(psi)/sin(fi)); y(i)=y(i)/pi; end; xmaxplot(x,y) axis equal; grid; title(‘R1=10.5mm,R2=13.5mm,gap=3mm’); print,

What is claimed is:
 1. A trough-shaped solar energy concentrator, thesolar energy concentrator being elongated along a longitudinal axis, thesolar energy concentrator comprising: a) an absorber configured toabsorb a light ray from the sun striking the absorber, the absorberdefining a polygon in cross section orthogonal to the longitudinal axis,the absorber being elongated along the longitudinal axis; b) areflector, the reflector being elongated along the longitudinal axis,the reflector having two reflector sides that are bilaterallysymmetrical about an optic plane, the two reflector sides definingopposing edges, the opposing edges defining an aperture between theopposing edges, the aperture being elongated along the longitudinalaxis, the aperture being configured to receive the light ray and toallow the light ray to pass to the reflector; c) each of the tworeflector sides distal to the absorber defining a curve normal to thelongitudinal axis, the curve being defined mathematically by a pluralityof curve points, each curve point being characterized by a junction of afirst line segment and a second line segment, the first and second linesegments each being mathematical and not being a physical object; d)wherein an end of the first line segment is fixed at a surface of theabsorber and the first line segment wraps about the absorber, for eachcurve point the first line segment is straight from the absorber to thecurve point, the first line segment defining a first line segment lengthfrom the end of the first line segment to the curve point; e) whereinfor each curve point an end of the second line segment is located on anedge line, the edge line being orthogonal to the light ray when thelight ray is at an acceptance angle at which the light ray passingthrough the aperture will be reflected onto the absorber by thereflector, the edge line being disposed between the absorber and the sunwhen the light ray is at the acceptance angle, wherein the second linesegment is parallel to the light ray at the acceptance angle, the secondline segment defining a second line segment length from the end of thesecond line segment at the edge line to the curve point corresponding tothe second line segment; and (f) wherein the sum of the lengths of thefirst and second line segments for each of the curve points is constant.2. The apparatus of claim 1, wherein the polygon is a square.
 3. Theapparatus of claim 1, wherein the polygon is a regular polygon.
 4. Theapparatus of claim 1, wherein the polygon is an irregular polygon.